High-fidelity simulations of plunging breaking waves are performed through direct numerical simulations of the two-phase air-water flow. We investigate how air is entrained during plunging breaking waves in the present study. It is responsible for the formation of numerous bubbles owing to the breakup of the entrained air. The energy dissipation due to viscosity is under consideration. It is found that most of the wave energy is lost after the wave breaking for a relatively large initial steepness. A coupled Level-Set and Volume of Fluid (CLSVOF) interface capturing method combining a high-order scheme based on WENO are adopted to compute moving interface. In order to gain more details, the block-based adaptive mesh refinement is used. Share surface tension model and a mass-momentum consistent scheme are also adopted for simulating high-density-ratio flows such as breaking waves. In addition, some wave breaking process including steep wave formation, jet overturning, air entrainment and splash up are well reproduced in the present study. The goal of the present research is to provide a detailed quantitative description of the air entrainment and energy dissipation in the plunging breaking waves.


Numerical simulation of breaking waves is more challenging. Two-dimensional plunging breakers were simulated and detailed breaking process are obtained by the Chen et al. (1999). Dalrymple and Rogers (2006) and Landrini et al. (2007) conducted the simulation of 2D plunging breakers using smooth particle hydrodynamics techniques. They concluded that the jet does not penetrate the free surface and bound up to form a forward splash. A plunging breaking wave without surface tension and viscous effects was simulated by Adams et al. (2010) using VOF method with 134 million grids. The overall plunging wave breaking process including the formation of vertical jet and oblique splash in the plunging wave breaking over a submerged bump was simulated by Kang et al. (2012). Recently, with the raid development of numerical methods and computer capability, more and more researchers’ interests focus the small structures in wave breaking. In the study by Wang et al. (2012), up to 2.2 billion girds are used to simulate the bow wave breaking around a wedge–shaped obstacle and this is the first attempt to investigate the wave breaking flows to the scale of micrometers. Almost 1 billion grids were used by Lubin & Glockner (2015) to study the fine vortex filaments which are generated at the early wave breaking stage. Wang et al. (2016) used very large grid (up to 12 billion grids) to perform the simulation of wave breaking process which focus on the small–scale structures such as bubble/droplet size distributions.

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